Prime Number Based Interleaver for Multiuser Iterative IDMA Systems

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					                    2010 International Conference on Computational Intelligence and Communication Systems
                   2010 International Conference on Computational Intelligence and Communication Networks

             Prime Number Based Interleaver for Multiuser Iterative IDMA Systems

                   Ruchir Gupta, B.K. Kanaujia                                          R.C.S. Chauhan, M. Shukla, Member IEEE
     Department of Electronics & Communication Engineering                                   Department of Electronics Engineering
               Ambedkar Institute of Technology                                              Harcourt Butler Technological Institute
                           Delhi, India                                                                  Kanpur, India

  Abstract—In recently proposed multiple access techniques such               each user. The system performance seriously degrades when
  as IDMA and OFDM-IDMA, the user separation is done by user                  the interleaving patterns are not orthogonal to each other i.e.
  specific interleavers in contrast to conventional CDMA scheme               the collision among the interleaving patterns is not minimum.
  where user separation is assured with user-specific signature               These interleavers disperse the coded sequences so that the
  sequences. The user specific interleavers must demonstrate                  adjacent chips are approximately uncorrelated, which facilitates
  minimum probability of collision amongst each other in addition             the simple chip-by-chip detection. In case of interleavers in
  to other merits including minimal consumption of bandwidth,                 IDMA systems, the parameters such as ease of generation,
  least hardware for their generation, and least memory                       hardware      required,     bandwidth     consumption      during
  requirement. Previously, random interleaver and other                       transmission, and memory requirement at transmitter and
  interleavers proposed by researchers is still leaving some space
                                                                              receiver end, may be vital parameters for generation of
  for further research leading to optimality of interleavers. In this
  paper, we propose a novel interleaver based on prime numbers
                                                                              orthogonal interleavers. The greater the size of interleaver the
  for generation of user specific interleavers to remove the problem          more it consumes the memory and extra bandwidth for
  of high consumption of bandwidth. The simulation results                    transmission, this becomes a greater problem when the number
  demonstrate the optimal performance of prime interleaver (PI)               of users increase. In [2], random interleaver has been utilized in
  apart from other merits in comparison to random and other                   IDMA systems, while in [4], an efficient technique for
  interleavers.                                                               interleaver generation in IDMA has been proposed in.
                                                                                  The second section highlights the IDMA systems model. In
      Keywords- prime numbers; computational complexity;
                                                                              third section, concepts of interleaving scheme along with
  interleaving; bandwidth requirement; memory requirement;                    various orthogonal interleavers are presented. In section 4, the
  orthogonality.                                                              proposed prime interleaver has been demonstrated while in
                                                                              section 5, the simulation results are demonstrated.
                         I.    INTRODUCTION
                                                                                                  II.   IDMA MECHENISM
      By researchers, significant amount of research has been
  done in the field of wireless communication. The recently                       IDMA does not involve signature sequences, which greatly
  developed techniques including iterative multi user detection               simplifies the problem of computational complexity in the
  (MUD) techniques for suppressing multiple access interference               receiver. The major difference between IDMA and CDMA is
  (MAI) [1-2] has also drawn their attention. Interleave division             regarding chip-level interleaving and bit level interleaving
  multiple access (IDMA) and OFDM-IDMA are the two                            respectively. It can be analyzed that the performance advantage
  multiple access (MA) schemes that make use of the iterative                 of IDMA increases with the number of users when compared to
  MUD efficiently, [3]. In IDMA, interleavers are being                       CDMA [1-2].
  employed as the only means of user separation while in CDMA                     In multipath channels, adjacent chips from each user
  the signature sequences were designed to be means of user                   interferes each other. In CDMA, the bits are spreaded and then
  separation as the spreader provides no coding gain [3]. With                passed with the same interleaver and transmitted consecutively,
  even random interleavers, the IDMA system performs similarly                so the corresponding log-likelihood ratios (LLRs) are heavily
  and even better than a comparable CDMA system [2]. IDMA                     correlated. In IDMA, however chip level interleaving is
  outperforms CDMA in terms of better immunity to multiple                    performed. After random chip level interleaving, the replicas
  access interference (MAI) and higher user count. IDMA also                  are dispersed more randomly, so the corresponding LLRs
  inherits the advantages of CDMA such as asynchronous                        become less correlated.
  transmission, diversity against fading and cross cell
  interference mitigation at a reduced cost of complexity [3] and                In order to minimize the forward error correction (FEC)
  high data rate. This chip by chip turbo type detection technique            code rate IDMA transmitter is employed. The key principle of
  in IDMA also reduces the complexity of receiver multi use                   IDMA is that the interleavers {Пk} should be user-specific i.e.
  detector (MUD) as compared to that used in CDMA system [2-                  the cross correlation between specific interleavers must me
  3].                                                                         minimum [7]. It is assumed that the interleavers are generated
                                                                              independently and randomly. These interleavers disperse the
     The efficiency of IDMA system is dependent on the                        coded sequences so that the adjacent chips are approximately
  generation of various pseudo random interleaving patterns for

978-0-7695-4254-6/10 $26.00 © 2010 IEEE                                 603
DOI 10.1109/CICN.2010.119
uncorrelated, which facilitates the simple chip-by-chip
detection scheme.
                                                                                 ζ k ( j ) = r ( j ) − hk x k ( j ) =   ∑h      k'
                                                                                                                                     xk ' ( j ) + n ( j )
                                                                                                                        k' ≠k

                                                                                is the distortion in r( j) with respect to user-k.
                                                                                 The output of ESE and DECOD-DESPREEADERs block
                                                                             is given as [2]

                                                                                                          r ( j ) − E ( r ( j )) + hk E ( xk ( j ))
                                                                              eESE ( xk ( j )) = 2 hk .                          2
                                                                                                              Var ( rj ) − hk Var ( xk ( j ))

                                                                              eDEC ( xk (π ( j ))) = ∑ eESE ( xk (π ( j )))
                                                                                                          j =1

                                                                                               j = 1,..., S

         Figure 1. Iterative IDMA Transmitter and Receiver
                                                                                III.    VARIOUS ORTHOGONAL INTERLEAVERS FOR IDMA
    Fig. 1 presents the transmitter and receiver structure of the                                     SCHEME
multiple access scheme under consideration with K                                 The principle of traditional periodic interleaving scheme
simultaneous users. The input data sequence dk of user-k is                  which is suitable to block codes can be expressed by
encoded based on a low-rate code C, generating a coded                       interleaving the data of array I × n. Let the interleaving degree
sequence ck [ck(1), . . . , ck(j), . . . , ck(J)], where J the frame         may be I for n bits. At the initial step, (I,n) linear block codes
length. The elements in ck are referred to as coded bits. The                are arranged in rows in an array I × n. Now, we transmit the
coded bits are further spreaded over entire bandwidth with the               array column by column. At the receiver, the received data are
help of spreader. The spreader may be counted to be common                   rearranged in the same array column by column, then decoding
or user specific. In this case, we have considered the spreader              it rank by rank.
to common to all the users. Then ck is permutated by an
interleaver k, producing xk [xk(1), . . . , xk(j), . . . , xk(J)].               In theory, the user-specific interleavers are generated
Following the CDMA convention, we call the elements in xk                    independently and randomly [2], known as random interleavers
“chips”. Users are solely distinguished by their interleavers;               (RI). In this case, the base station (BS) has to employ a
hence     the    name      interleave-division multiple-access               considerable amount of memory to store these interleavers at
(IDMA).The chip interleavers allow adopting a chip – by-chip                 transmitter and receiver side, which may cause serious concern
estimation technique [2].                                                    in case of large user count. Also, during the initial link setting-
                                                                             up phase, there should be messages passing between the BS
    At the receiver side, the outputs of the elementary signal               and mobile stations (MSs) to inform each other about user
estimator`s (ESE) and DECOD-DESPREEADERs are extrinsic                       specific interleavers. Extra bandwidth resource will be
log-likelihood ratios (LLRs) about {xk }defined as [2]                       consumed for this purpose if the interleavers used by the BS
                                                                             and MSs are long and randomly generated. In [5], master
                                                                             random interleaver or power interleaver generation method is
                         ⎛ p ( y / xk ( j ) = +1) ⎞                          presented to alleviate this concern. With this method, the
      e( xk ( j )) = log ⎜                        ⎟ , ∀k , j. (1)            interleaver assignment scheme is simplified and memory cost
                         ⎝ p ( y / xk ( j ) = −1) ⎠                          is greatly reduced without sacrificing performance, but the
                                                                             complexity for regeneration of interleavers and deinterleavers
   These LLRs are further distinguished by the subscripts i.e.,              at the receiver side is major concern in case of higher user
eSEB ( xk ( j )) and eDEC ( xk ( j )) , depending upon whether               count [7] provided that enough memory space is not used to
they are generated by ESE and DECOD-DESPREEADERs.                            store all required interleavers.

    Due to the use random interleavers {Π k}, the ESE                            Researchers has proposed various other interleavers in [8-
operation can be carried out in a chip-by-chip manner, with                  13][15][16]. PEG interleaver generation mechanisms [8]
only one sample r(j) used at a time. The received signal at the              explain the selection of suitable orthogonal interleavers out of
receiver is given as                                                         pre-generated random interleavers while other mechanisms
                                                                             including [9-13], [15-16] explain the independent generation of
                                                                             orthogonal interleavers which are losing their orthogonality in
           r ( j ) = hk xk ( j ) + ζ k ( j )     (2)                         case of higher user count. In [7], tree base interleaver (TBI)
                                                                             generation scheme is presented which employs two master
                                                                             interleavers, which are randomly selected. User specific
   where                                                                     interleaver is designed using a combination of both master

interleavers. The scheme is optimum in terms of bandwidth                      The bandwidth required by the Prime Interleaver (PI) is
requirement and BER [14]; however, still there is space for                 smaller than other available interleavers as now only seed is to
development of other efficient interleavers for IDMA scheme.                be transmitted, in addition to very small amount of memory
                                                                            required at the transmitter and receiver side as shown in table
    Here, in this paper, a new interleaver is proposed based on             1.
prime number which gives a novel user-specific interleaver
generation mechanism with lesser time to get it generated and                    TABLE I COMPARISON OF BANDWIDTH REQUIREMENT FOR
along with minimal consumption of bandwidth required during                                                                                                                  TRANSMISSION OF THE INTERLEAVING MASK
transmission well similar performance in terms of BER to that                     User                                                                                                 Random                         Tree Based                          Prime
of random interleaver.                                                            Count                                                                                               Interleaver                     Interleaver                       Interleaver
                                                                                                                                                                                      Generation                      Generation
                                                                                                                    2                                                                      2                               2                                     1
            IV.     MECHANISM OF PRIME INTERLEAVER                                                                  6                                                                        6                                 2                                 1
    In IDMA, different users are assigned different interleavers                    14                                                                                                       14                                2                                 1
which are weakly correlated. The computational complexity                           30                                                                                                       30                                2                                 1
and memory requirement should be small for generation of
                                                                                   62                                                                                                      62                                  2                                 1
interleavers. The Prime Interleaver is basically aimed to                          126                                                                                                     126                                 2                                 1
minimize the bandwidth and memory requirement that occur in
other available interleavers with bit error rate (BER)
performance comparable to random interleaver.                                                                                                                            x 10
                                                                                                                                                                                       Comparison Graph showing Bandwidth Requirement of 4 Interleavers
    In generation of prime interleaver we have used the prime                                                                                                                                                       Bandwidh requirement of Random Interleaver

numbers as seed of interleaver. Here, user-specific seeds are                                                                                                      4.5
                                                                                                                                                                                                                    Bandwidth requirement of Master Random Interleaver
                                                                                                                                                                                                                    Bandwidth requirement of Tree Based Interleaver

                                                                                    B an dw idt h R eq uirem ent of Int erleav er(N o.of bits requ ired/u s e r)
assigned to different users.                                                                                                                                        4
                                                                                                                                                                                                                    Bandwidth requirement of Prime Interleaver

    For understanding the mechanism of prime interleaver, let
us consider a case of interleaving n bits with seed p. First, we
consider a Gallois Field GF (n). Now, the bits are interleaved                                                                                                      3

with a distance of seed over GF (n). In case, if {1, 2, 3, 5, 6, 7,
8… n} are consecutive bits to be interleaved with seed p then                                                                                                      2.5

location of bits after interleaving will be as follows                                                                                                              2

      1===> 1                                                                                                                                                      1.5

      2===> (1+p) mod n                                                                                                                                             1

      3===> (1+2p) mod n                                                                                                                                           0.5

      4===> (1+3p) mod n                                                                                                                                            0
                                                                                                                                                                         0       10     20        30        40        50     60          70        80       90           100
      .         .                                                                                                                                                                                                User Number

      .         .                                                             Figure 2. Comparison of Bandwidth requirement of various interleavers
      .         .
                                                                                In master random interleaving scheme the computational
      n===> (1+(n-1)p) mod n                                                complexity and transmitter and receiver end is quite high due
                                                                            to calculation of user-specific intereleaving masks. The prime
    For Example if we have to interleave 8 bits such that {1, 2,
                                                                            interleaving scheme reduces the computational complexity that
3, 4, 5, 6, 7, 8} and we wish to interleave these bits with seed 3
                                                                            occurs in master random interleaving scheme; however, it is
then the new location of bit will be as follows
                                                                            higher to that of tree based interleaving scheme due
      1===> 1                                                               computation involved for calculation of user specific
      2===> (1+1*3) mod 3===>4
      3===> (1+2*3) mod 3===>7                                                                                                                                                         V.           NUMERICAL RESULTS
      4===> (1+3*3) mod 3===>2                                                  For simplicity, IDMA system with BPSK signaling in
      5===> (1+4*3) mod 3===>5                                              AWGN channel for hk=1, ∀ k is assumed. Without loss of
                                                                            generality, a uniform repetition coding CREP {+1, -1, +1, -1, ----
      6===> (1+5*3) mod 3===>8                                              -----} is used with spread length sl =16, for all users. In figure
                                                                            3, uncoded IDMA cases are considered, i.e., without any
      7===> (1+6*3) mod 3===>3
                                                                            forward error correction (CFEC) coding while data length is
      8===> (1+7*3) mod 3===>6                                              taken to be 512. In figure 5, Memory-2 Rate-1/2 Convolutional
                                                                            code is used. The iteration at the receiver side is chosen to be
      Now, the new order of bits will be {1, 4, 7, 2, 5, 8, 3, and          15 in each case.

    From these figures, it is evident that the BER performances                                                                               CDMA under same conditions, results are better with IDMA
of IDMA scheme are similar for random and prime                                                                                               scheme as number of users is increased [2].
interleavers. But from figure 2, it is clear that, on the front of
                                                                                                                                                 In figure 4, the coded IDMA for 16 users have been
bandwidth consumption, the prime interleaver is outperforming
                                                                                                                                              presented along with results in uncoded as well coded IDMA
the other interleavers because only the user specific prime
                                                                                                                                              environment. The result shows similar BER performances of
numbers have to be sent along with data format during
                                                                                                                                              prime interleavers to random interleavers in coded as well
                                                                                                                                              uncoded IDMA environments. The simulation results for coded
                                                                                                                                              IDMA systems outperform the uncoded IDMA systems when
                            10                                                                                                                compared in terms of bit error rate (BER) performance. The
                                                                                                                                              prime interleaver is, however, performing similar to that of
                                                                                                                                              random interlevers.

                                                                                                                                                                         VI.     CONCLUSION
                                                                                                                                                  The proposed ‘Prime Interleaver’ is very easy to generate
                                      Prime Interleaver 1 user
                                      Random Interleaver 1 user                                                                               and is better than the random or any other interleavers in terms
        B it E rror Rate

                                      Random Interleaver 4 users
                                      Prime Interleaver 4 users
                                                                                                                                              of bandwidth consumption problems. The Prime interleaver is
                                                                                                                                              better than master random interleaver in terms of
                                      Random Interleaver 8 users
                                      Prime Interleaver 8 users
                                      Random Interleaver 16 users
                                                                                                                                              computational complexity. With tree based interleaver, the
                            10        Prime Interleaver 16 users                                                                              proposed interleaver seems to be having little bit more
                                      Prime Interleaver 24 users
                                      Random Interleaver 24 users
                                                                                                                                              complexity due to involvement of higher calculation for
                                      Random Interleaver 32 users                                                                             calculation of user-specific interleavers.
                             -5       Prime Interleaver 32 users
                                      Random Interleaver48 users                                                                                  The BER performance of all the interleavers including
                                      Prime Interleaver 48 users
                                      Random Interleaver 64 users                                                                             random interleaver and tree based interleaver is almost similar.
                                      Prime Interleaver 64 users
                                                                                                                                              However, entertaining the other issues including memory and
                                  2       4            6                8
                                                                                    10               12            14              16
                                                                                                                                              bandwidth requirements, the proposed interleavers seems to be
                                                                                                                                              optimum and can take the place of the random or any other
 Figure 3. Performance comparison of Prime Interleaver (PI) with Random
                                                                                                                                              interleaver techniques without performance loss in IDMA
                Interleaver (RI) in uncoded IDMA systems                                                                                      systems.

                                                                                             Prime Interleaver 16 users Coded
                                                                                             Random Interleaver 16 users Coded
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Description: In recently proposed multiple access techniques such as IDMA and OFDM-IDMA, the user separation is done by user specific interleavers in contrast to conventional CDMA scheme where user separation is assured with user-specific signature sequences. The user specific interleavers must demonstrate minimum probability of collision amongst each other in addition to other merits including minimal consumption of bandwidth, least hardware for their generation, and least memory requirement. Previously, random interleaver and other interleavers proposed by researchers is still leaving some space for further research leading to optimality of interleavers. In this paper, we propose a novel interleaver based on prime numbers for generation of user specific interleavers to remove the problem of high consumption of bandwidth. The simulation results demonstrate the optimal performance of prime interleaver (PI) apart from other merits in comparison to random and other interleavers.